The present invention generally relates to semiconductor devices and more particularly to a quantum semiconductor device that uses a quantum point contact for producing a quantum mechanical carrier wave with directivity.
Recent development of epitaxial processes such as MBE or MOCVD has enabled the growth of substantially defect-free crystals. In such high quality crystals, the mean-free path of the carriers has been increased significantly. For example, the electrons can now be transported ballistically for a length of as much as 10 .mu.m without experiencing substantial scattering. On the other hand, the progress of fine lithographic patterning technology has enabled the fabrication of semiconductor devices that have a device pattern substantially smaller than 1 .mu.m. For example, the currently available patterning process can form a device structure wherein the carriers such as electrons or holes are confined in a submicron region having a lateral size in the order of 0.1 .mu.m. When the carriers are confined in such a small region the size of which is comparable to the de Broglie length, the wave nature of carriers becomes conspicuous.
Thus, intensive efforts are being made to realize the so-called quantum semiconductor devices that use the wave nature of carriers positively for the device operation. It should be noted that this type of device is distinguished over the conventional quantum semiconductor devices, which confine the carriers in a thin epitaxial layer (for example, Esaki et al., IBM Research Note, RC-2418, 1969), in that the confinement of the carriers is achieved laterally by creating a depletion region. Such a depletion region is created typically by a Schottky electrode. By controlling the lateral extension of the depletion region in response to the voltage applied to the Schottky electrode, one can control the size of the region where the carriers are confined and hence the quantum levels formed therein. Thereby, the operational characteristics of the device is controlled variously.
FIG. 1 shows a conventional quantum semiconductor device proposed by the inventor of the present invention.
Referring to FIG. 1 showing the device in a plan view, the device includes a channel region 14 that has a cross sectional view substantially identical with that of a HEMT. Thus, there is formed a two-dimensional carrier gas along a heterojunction interface that characterizes the HEMT. On the upper major surface of the channel region 14, there is provided a Schottky electrode 10 that is formed with a gap 12, and a depletion region 16 is formed in correspondence to the Schottky electrode 10 as indicated by a broken line. There, the depletion region 16 is interrupted in correspondence to the gap 12 and there is formed a passage of the carriers in correspondence to the gap 12 with a lateral extension L that changes in response to the electric voltage applied to the electrode 10. The lateral extension L is set approximately equal to or smaller than the de Broglie length of the carriers, and there are formed discrete quantum levels in the passage of the carriers. On the other hand, the passage has a length, measured perpendicularly to the elongating direction of the electrode 10, such that the length is set smaller than any of the elastic and inelastic scattering lengths of the carriers. Thereby, the passage forms a quantum point contact as reported by Van Wees et al. (Van Wees, B. J., et al., Physical Review Letters, Vol. 60, No. 9, 1988).
The quantum point contact is supplied with carriers, and each carrier thus supplied behaves as a quantum mechanical wave in the quantum point contact because of the lateral carrier confinement. Thereby, the carriers are emitted from the quantum point contact in the form of the quantum mechanical wave that is characterized by a directional radiation pattern, wherein the directivity of the radiation pattern is changed in response to the lateral extension L of the quantum point contact.
In order to supply the carriers to the quantum point contact, there is provided an emitter electrode 2 on the upper major surface of the channel region 14, while there are provided collector electrodes 4, 6 and 8 in contact with the upper major surface of the channel region 14 for collecting the carriers that have been emitted from the quantum point contact. By controlling the directivity of the radiation pattern in response to the electric voltage that is applied to the Schottky electrode 10, one can control the operational conditions of the device, between a first state wherein the electrode 6 detects the carriers and a second state wherein the electrodes 4 and 8 detect the carriers.
FIGS. 2(A) and 2(B) show the principle of formation of the quantum mechanical carrier wave in the quantum point contact for two different settings of the size L of the quantum point contact. As already explained, there are formed discrete quantum levels in the quantum point contact as a result of the lateral confinement of the carriers. In the description below, the x-y coordinate system defined in FIG. 1 will be employed.
Referring to FIG. 2(A) showing the case where the size L of the quantum point contact is set small enough such that quantum level E.sub.1 corresponding to the ground state of the discrete quantum levels is formed below the Fermi energy E.sub.F of the incident carriers such that the Fermi energy E.sub.F is located above the quantum level E.sub.1 but below the quantum level of a higher quantum state, there appears a wave function .phi..sub.1 (y) in correspondence to the quantum level E.sub.1 wherein the wave function .phi..sub.1 (y) is represented by a symmetric function such as A.multidot.cos(.pi..multidot.y/L) in correspondence to the standing wave formed in the quantum point contact, where A is a constant. Thereby, the wave function .phi..sub.1 (y) has a node at both ends in correspondence to the lateral boundaries of the quantum point contact. Further, the wave function .phi..sub.1 (y) has an antinode in correspondence to the central part thereof. Thus, the carrier wave for this mode lacks the component that propagates in the y-direction and the incident electron beam propagates through the quantum point contact straight in the x-direction with a wave vector k.sub.x1 that is given by EQU n.sup.2 .multidot.k.sub.x1.sup.2 /2m.sup.* =(E.sub.F -E.sub.1), (1)
where n represents the Planck's constant divided by 2.pi. and m.sup.* represents the effective mass of the carrier particle.
In the case where the size of the quantum point contact is increased to L' as shown in FIG. 2(B), the Fermi level E.sub.F for the incident carriers is located above a quantum level E.sub.2 that is formed above the quantum level E.sub.1 as a higher order quantum state. In correspondence to the quantum level E.sub.2, there appears a wave function .phi..sub.2 (y) that is represented by an asymmetric function such as A.multidot.sin(2.pi..multidot.y/L) in correspondence to the higher order harmonics. There, the wave function .phi..sub.2 (y) includes a node at the central part thereof, and the phase of the wave function changes by 180 degrees across the central node. It should be noted that such an inversion of the phase indicates that there exits a wave component propagating in the y-direction in the mode of FIG. 2(B), in addition to the component that propagates in the x-direction. There, the wave vector k.sub.x2 for the x-component satisfies a relationship ##EQU1## wherein the wave vector k.sub.y2 is determined by the size L' of the quantum point contact. When the wave vector k.sub.y is determined, the wave vector k.sub.x is determined by Eq. (2). Thereby, the carrier wave exits from the quantum point contact and travels away therefrom while maintaining the waveform of the wave function .phi..sub.2 (y).
It should be noted that the device of FIG. 1 has the collector electrode 6 provided in alignment with the quantum point contact for detecting the carriers that have passed through the quantum point contact with the ground state shown in FIG. 2(A). On the other hand, the collector electrodes 4 and 8 are provided for detecting the carrier waves for the second quantum state shown in FIG. 2(B). It should be noted that the carrier waves corresponding to the wave function .phi..sub.2 (y) are emitted in two directions that are symmetrical with respect to the x-axis.
By applying an input voltage to an input terminal IN connected to the Schottky electrode 10 with a voltage level adjusted suitably, it is possible to realize the state shown in FIG. 2(A). Thereby, an output signal is obtained at an output terminal OUT1 that is connected to the collector electrode 6. When the voltage to the Schottky electrode 10 is set to a second voltage that is adjusted to realize the state shown in FIG. 2(B), an output signal is obtained at an output terminal OUT2 that is connected to the collector electrodes 4 and 8.
FIG. 3 shows the angular radiation profile of the carrier wave that is generated by the quantum point contact, wherein the broken line designated as F.sub.1 corresponds to the radiation formed by the wave function .phi..sub.1 while the two broken lines designated as F.sub.2 correspond to the radiation formed by the wave function .phi..sub.2. It will be noted that only the profile of F.sub.1 is obtained when the device is biased as shown in FIG. 2(A), while the radiation patterns F.sub.1 and F.sub.2 overlap with each other when the device is biased as shown in FIG. 2(B). Thereby, the overall output profile of the device in the biasing state of FIG. 2(B) is represented by the continuous line shown in FIG. 3 (Okada et al., "Angular Distribution of Electrons Injected Through A Quantum Point Contact" Superlattice and Microstructures, Vol. 10, No. 4, 1991). From FIG. 3, it will be noted that the change of the output signal between the state of FIG. 2(A) and the state of FIG. 2(B) is relatively small due to the overlapping of the radiation profiles F.sub.1 and F.sub.2. Thereby, there exists a substantial difficulty in constructing a logic circuit based upon the device of FIG. 1.